Center cyclicity of a family of quartic polynomial differential system

Isaac A. García; Jaume Llibre; Susanna Maza

doi:https://doi.org/10.1007/s00030-016-0388-8

Center cyclicity of a family of quartic polynomial differential system

Isaac A. García, Jaume Llibre, Susanna Maza

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

© 2016, Springer International Publishing. In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as (Formula presented.), where A, B, C∈ C. We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp.

Original language	English
Article number	34
Journal	Nonlinear Differential Equations and Applications
Volume	23
Issue number	3
DOIs	https://doi.org/10.1007/s00030-016-0388-8
Publication status	Published - 1 Jun 2016

Keywords

Bautin ideal
Center
cyclicity
limit cycle
polynomial vector fields

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AU - Llibre, Jaume

AU - Maza, Susanna

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N2 - © 2016, Springer International Publishing. In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as (Formula presented.), where A, B, C∈ C. We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp.

AB - © 2016, Springer International Publishing. In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as (Formula presented.), where A, B, C∈ C. We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp.

KW - Bautin ideal

KW - Center

KW - cyclicity

KW - limit cycle

KW - polynomial vector fields

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